Is it possible to do K-nearest-neighbours before training DNN
There are two factors that will change the ability of a deep neural network to fit a given dataset: either you need more data, or a deeper and wider network. Since the pattern is only 2-d, it can likely be approximated by some sort of simple periodic function. A DNN can approximate periodic functions pretty well, so the issue is probably that you don't have enough data. 

If you have an apriori belief that the pattern is well approximated by K-nearest neighbors, then you could do the following:


Fit a K-NN model to the data.
Generate $N$ new points uniformly at random from the input space.
Label the $N$ new points using the K-NN model.
Fit your DNN to the original dataset, plus the $N$ new points.